2. The Exponential Trendline of Economic Growth

Study the past, if you would divine the future.

– Confucius

The future influences the present just as much as the past.

– Friedrich Nietzsche

(Video). The first and most important concept to internalize is the accelerating rate of change. This is a very under-discussed subject even though it increasingly affects almost everything about modern life. One of the best places to read about this is Ray Kurzweil’s 2001 essay, despite the age of the article (the dearth of more recent writings by multiple people is itself a problem that this whitepaper aims to correct). From his essay, we see how technological progress is accelerating, multi-faceted, and diverse. The essay also proves that technological progress is not in stagnation or reversal, as some claim. It is important to note how exponentially accelerating processes have been going on since the dawn of life on Earth, and through the evolution of life, with each unit of change taking even smaller intervals of time. That process has continued through measures of progress within human society as well, especially in economics and technology. In this chapter, we will specifically focus on the economic side of accelerating change, for no other metric does more to demonstrate how fortunate we are to be alive in the 21stcentury.

Economic Growth Through the Ages : Everyone has studied historical events in school, passing exams and even writing papers. Contemporary schooling barely describes the greatest historical transformation of all time – the very recent upliftment of the human condition. An education about historical events is utterly incomplete without a sufficient illustration of the prosperity levels of the era. This backdrop has to go far deeper than a ‘there were no airplanes in those days’ level of cursory mention, for only then can the conditions precipitating wars over resources, slavery, etc. be truly grasped. Romanticizing the imagery of some past society invariably necessitates a selective focus on the topmost aristocrats, while ignoring the brutal and brief lives that the other 99% were condemned to. Effectively, any lament about ‘how good things were then’ is an inaccurate fictionalization.

We are presently accustomed to per capita real growth rates of almost 3%/year for the world economy and consider this to be a status quo cruising speed, as though such a growth rate has always existed. In reality, such growth rates did not begin until the middle of the 20th century. In the 19th century, the average world growth rate was much lower, at about 1%/year. Before that, annual growth rates were a fraction of 1% from the 16th through the 18th centuries, and virtually 0% for the thousands of years of human civilization before that. The accelerating rate of economic growth (which is the second derivative, mind you) has not stopped, despite how lackluster present conditions may feel.

Let us examine the above two charts (click to expand), which indicate world GDP per capita in current dollars first on a linear scale and then on a logarithmic scale, 1960-2014. The exponential nature of economic growth is apparent from both charts, but each depicts the trajectory in a different light. If you projected the same trend forward just a few more years, we can see that a much higher level of prosperity arrives. The topic of adjusting for inflation may arise, but as we will see in a later section, current methods of calculating inflation overstate inflation rates, and are thus starting to become obsolete.

We have world GDP estimates going back centuries, and if we take a simple linear regression of past data and project it until the year 2050, on a third chart with a logarithmic scale on the vertical axis, we get a window into the future. We can examine this even more effectively with the horizontal axis oriented as looking backwards from the present. Note the parabolic curve despite the scale being logarithmic, effectively exhibiting a second derivative of exponential growth. The accelerating nature of economic growth, going back centuries, is apparent when the chart is presented in this way, and proves that it could not have existed until recently.

Imagine if 3% annual growth rates in per capita GDP, implying a doubling every 24 years, had started from 500BC, resulting in over 105 doublings by now. Or from 1500 AD or even from 1800 AD, which would still have yielded nine doublings since then, resulting in a growth factor of an incredible 512x. Since growth rates of this nature were never possible before the modern era, the second-derivative indicates that there is no reason to think the trendline has stopped or even plateaued. The key word here is trendline, as distinct from actual data.

If thousands of years of nearly 0% growth can be followed by a century of 1%, several decades of 2%, and then another few decades of 3% growth, simple mathematical extrapolation of that trend implies much higher growth rates in the near future. This fourth chart is an extension of the same chart backwards 2500 years. As we can see, the steep trajectory of growth has never, at any time, halted or reversed. In terms of simple multipliers, the rise from 1% to 3% trendline growth is no different, proportionally, than a rise from 3% to 9% growth later on in the curve. Mathematically, this should not ‘seem’ any more rapid for the estimated year the curve intersects than today’s growth rates would have seemed in the 19th century. You may be skeptical about this if you have not read the later chapters in this whitepaper yet. Is an unstoppable progression of ever-rising growth rates a believable outcome? Since past performance is not always a predictor of future outcomes, surely we cannot just project the trendline to a point where in just a few decades even ordinary people are destined to have great prosperity. Is there some ceiling of human productivity that we have arrived at? How will most people acquire the skills to produce that much output? Is it not inevitable for the law of large numbers to eventually catch up, even if an identical skeptic in the 19th century would have been proven wrong had he dismissed an accurate prediction of 2015 prosperity as too optimistic?

The crucially unpredictable ingredient in such projections is that of nation-state risk. Economic growth within an individual country does not just happen without the right set of conditions. Sometimes, the wrong policies, centralized micromanagement, or ossified assumptions can lead to economic declines such as the Great Depression. Recoveries since these calamities have generally returned world GDP back to the trendline as though the crisis never happened, but some nations often leapfrog others in the process, capturing a disproportionate share of the recovery. The most prominent example is of how China and India jointly declined from being 40% of world GDP in 1820 to just 2% in 1975, even as the aggregate world GDP trendline was a smooth exponential curve throughout that period. This period was essentially the ‘Dark Ages’ for China and India, precisely coinciding with when the West was outperforming by the greatest margin. The rapid recoveries of China and to a lesser extent India since then can be seen as the start of a process of mean reversion to historical norms of GDP share, assisted by the steeply rising world trendline. The two nations are now jointly 18% of world GDP, and may very well recover all the way up to the traditional 40% in a matter of just years, not decades or centuries.

Thus, there is reason to believe that if governments adjust policies accordingly and proactively, world GDP per capita can be restored to the trendline. There is similar reason to believe that the economy may force a toppling of obstacles preventing the trendine from reverting back to its natural state. So far, this trajectory has reverted to the exponential trendline through world wars, economic depressions, plagues, and the dissolution of empires.

Yet most developed countries today somehow appear to be stuck in a lengthy malaise of sub-par growth, combined with little or no inflation. There seems to be a resigned acceptance of a melancholy ‘Real’ per capita growth rate of under 2% in the US, and under 1% in Europe, even though this is less than what was seen in the 1990s. The default assumption appears to be that this will be the norm for the foreseeable future, in direct violation of the expected accelerating gradient of growth. Even worse, the Nominal GDP that the US normally sees has fallen from over 6% prior to 2007 to under 4% now, which adds a poorly understood but nonetheless substantial damper on economic vibrancy and the pace of innovation. As more years of this divergence accumulate, the opportunity cost is rising. The world can no longer afford to continue to ignore how technology has altered the fundamentals of macroeconomics.

Comments

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One thought has troubled me for some time in measuring wealth and growth. In the past there was a long way to go for someone to feel wealthy. There were tangible improvements to lifespan, health, welfare, etc. associated with great wealth. Therefore increases in GDP were directly tied to the happiness of people, and tangible improvements to their lives.

What is it like when we live in a world where being a millionaire is not a particularly important accomplishment? I live in a modest neighborhood, and my neighbor is fairly wealthy. he stills lives in his modest, but greatly improved, house. He also has a vacation home in a sunnier clime. He has a nice car. But...he admits, he doesn't really have any use for most of his wealth. He literally cannot not consume enough things to diminish it, or even put a dent in it.

How does this impact GDP? When more and more people have all their modest materiel wants satisfied?

My neighbor, when he made enough money to be comfortable (not more than $5 million), stopped working for the most part. Oh he plays around a bit, but really, he doesn't work that hard. Not as hard as he did when he made his money. he is underproductive, and is an underperforming asset. he is a drag on the growth of GDP. whatever avarice he once had is gone. he has satisfied all his needs. At best he works part time.

I guess the point I'm trying to make is that accumulated wealth slows growth. Success doesn't always build on success, it can lead to stagnation. My neighbor is the very definition of doing less with more, which is not something most economists consider.

"Is there some ceiling of human productivity that we have arrived at?" Yes, based on my example, I think so. The limit is us unfortunately - how much we can or want to consume. All exponential growth curves eventually morph into S-curves.

"Sometimes, the wrong policies, centralized micromanagement, or ossified assumptions can lead to economic declines such as the Great Depression." or Venezuela. seriously, could there be a better example of how government policies and economic mismanagement can roll back prosperity? Venezuela was, for decades, a decidedly middle income country. Now it is a basket case. In less than a decade, utterly ruined.

Another strange effect of technology is people "feeling" wealthier than they truly are. For example, overseas travel used to be for the rich and famous. Then became a middle income activity with cheap jet travel. Now...with VR, anyone can see whatever part of the world they wish. Sure you could still go there, but the point is that you feel richer, that the poor can do more, experience more with even a limited income.

So I guess part of what may be hurting nominal GPD is the mere fact that it no longer accurately measures our wealth. Upper middle income people feel progressively more wealthy due to technology, and because of this take their foot off the gas, much like my neighbor did.

I guess, to summarize further, I'm saying that GDP growth is in part psychological. It is driven by human wants and desires. These are not exponential, and have quantifiable limits.

Yes, there are many limits to GDP as a metric. Even more than some people feeling wealthy (most of the ultrawealthy still work hard), part of the problem is in the manner it is calculated.

There are a variety of new products your neighbor can buy when innovation makes them available, such as household robots to clean the bathroom (replacing the person he hires), longevity treatments, self-driving cars (which will have a high premium for a while still), etc.

VR does indeed commoditize many types of recreation and experiences, as the brain will 'feel' as though the person has indeed done that thing for real. Not many understand the disruptive effect of VR on seemingly unrelated things like real estate prices, the travel industry, male-female interactions, etc.

Btw, can you give an estimate from ATOM's point of view why the world GDP per capita growth has stagnated from 1994 to 2002. That was the time of personal computer s becoming mainstream and spectacular show of Moore's law. And yet the char shows a decade of virtually no growth...

Btw, can you give an estimate from ATOM's point of view why the world GDP per capita growth has stagnated from 1994 to 2002.

It was due to the wind down and breakup of the USSR, which led to low GDP growth in all associated countries for the following decade. It was also due to a brief dollar strengthening due to cheap oil and US technology exports.

Note how GDP still reverted back to the trendline sharply thereafter. The trendline is what matters, always..

KG,
I would expect cheap oil and techno exports to be a net increase to the GDP. Do you think that it was a deflationary pressure of the technology/atom that shows reduced growth?
And a more interesting question is do we have something like that in store for the up upcoming decade?

The cheap oil strengthened the dollar briefly due to the US being the biggest oil importer by far at the time, and this is a $USD metric of GDP. So it does see short-term fluctuation due to currency rates.

PPP removes this problem, but introduces others, so the nominal ($USD) metric is still better.

For the upcoming decade, NGDP will continue to contract until the ATOM forces a major market correction that increases the level of central bank monetary expansion. Since GDP is below the trendline again (even as the trendline itself is steeper than it was in 1994-2002), we will see a reversion up. But this reversion up may require a major recession first to open the floodgates of QE..

India is the last major country to see a one-time currency gain (which China experienced 2005-12). This will increase the US$ GDP of India from $2.5T today to $10T faster than anyone thinks (just as China covered this distance in just 7-8 years)...

Has the author of this article ever considered the existence of biophysical limits to endless economic growth?

I am not aware of a single study, simulation or any kind of evidence demonstrating that GDP will ultimately be decoupled from energy and material use.

This matters, a lot! It suffices to take a closer look at the Planetary Boundaries framework first introduced by Rokstrom (2009). Essentially, we have already surpassed many of the safety zones for planetary boundaries such as atmospheric carbon dioxide, biodiversity loss and anthropogenic nitrogen removed from the atmoshpere. And already, we are quickly approaching the boundaries for saturation of aragonite in surface seawater (ocean acidification) and land surface converted to crop land.

The world, still lead by cornucopians and technology-enthusiasts, can no longer afford to ignore how earth processes and how their carrying capacity for human activities pose fundamental limits on economic growth in the medium run.